A distributed forward-backward algorithm for stochastic generalized Nash equilibrium seeking

Barbara Franci; Sergio Grammatico

doi:10.1109/TAC.2020.3047369

A distributed forward-backward algorithm for stochastic generalized Nash equilibrium seeking

Barbara Franci, Sergio Grammatico

Team Bart De Schutter

Research output: Contribution to journal › Article › Scientific › peer-review

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Abstract

We consider the stochastic generalized Nash equilibrium problem (SGNEP) with expected-value cost functions. Inspired by Yi and Pavel (2019), we propose a distributed generalized Nash equilibrium seeking algorithm based on the preconditioned forward-backward operator splitting for SGNEPs, where, at each iteration, the expected value of the pseudogradient is approximated via a number of random samples. Our main contribution is to show almost sure convergence of the proposed algorithm if the pseudogradient mapping is restricted (monotone and) cocoercive.

Original language	English
Pages (from-to)	5467-5473
Journal	IEEE Transactions on Automatic Control
Volume	66
Issue number	11
DOIs	https://doi.org/10.1109/TAC.2020.3047369
Publication status	Published - 2021

Bibliographical note

Accepted Author Manuscript

Keywords

Approximation algorithms
Convergence
Cost function
Nash equilibrium
Random variables
stochastic approximation
Stochastic generalized Nash equilibrium problems
Stochastic processes
Uncertainty
variational inequalities

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10.1109/TAC.2020.3047369

A_distributed_forward-backward_algorithm_for_stochastic_generalized_Nash_equilibrium_seekingAccepted author manuscript, 476 KB

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title = "A distributed forward-backward algorithm for stochastic generalized Nash equilibrium seeking",

abstract = "We consider the stochastic generalized Nash equilibrium problem (SGNEP) with expected-value cost functions. Inspired by Yi and Pavel (2019), we propose a distributed generalized Nash equilibrium seeking algorithm based on the preconditioned forward-backward operator splitting for SGNEPs, where, at each iteration, the expected value of the pseudogradient is approximated via a number of random samples. Our main contribution is to show almost sure convergence of the proposed algorithm if the pseudogradient mapping is restricted (monotone and) cocoercive.",

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AU - Grammatico, Sergio

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N2 - We consider the stochastic generalized Nash equilibrium problem (SGNEP) with expected-value cost functions. Inspired by Yi and Pavel (2019), we propose a distributed generalized Nash equilibrium seeking algorithm based on the preconditioned forward-backward operator splitting for SGNEPs, where, at each iteration, the expected value of the pseudogradient is approximated via a number of random samples. Our main contribution is to show almost sure convergence of the proposed algorithm if the pseudogradient mapping is restricted (monotone and) cocoercive.

AB - We consider the stochastic generalized Nash equilibrium problem (SGNEP) with expected-value cost functions. Inspired by Yi and Pavel (2019), we propose a distributed generalized Nash equilibrium seeking algorithm based on the preconditioned forward-backward operator splitting for SGNEPs, where, at each iteration, the expected value of the pseudogradient is approximated via a number of random samples. Our main contribution is to show almost sure convergence of the proposed algorithm if the pseudogradient mapping is restricted (monotone and) cocoercive.

KW - Approximation algorithms

KW - Convergence

KW - Cost function

KW - Nash equilibrium

KW - Random variables

KW - stochastic approximation

KW - Stochastic generalized Nash equilibrium problems

KW - Stochastic processes

KW - Uncertainty

KW - variational inequalities

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DO - 10.1109/TAC.2020.3047369

M3 - Article

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SN - 0018-9286

VL - 66

SP - 5467

EP - 5473

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 11

ER -

A distributed forward-backward algorithm for stochastic generalized Nash equilibrium seeking

Abstract

Bibliographical note

Keywords

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